Near-Optimal Private Learning in Linear Contextual Bandits

We analyze the problem of private learning in generalized linear contextual bandits. Our approach is based on a novel method of re-weighted regression, yielding an efficient algorithm with regret of order $\sqrt{T}+\frac{1}{\alpha}$ and $\sqrt{T}/\alpha$ in the joint and local model of $\alpha$-privacy, respectively. Further, we provide near-optimal private procedures that achieve dimension-independent rates in private linear models and linear contextual bandits. In particular, our results imply that joint privacy is almost "for free" in all the settings we consider, partially addressing the open problem posed by Azize and Basu (2024).